Question: Simplify the following expression: $ k = \dfrac{-10n + 5}{-8n - 6} - \dfrac{-10}{9} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-10n + 5}{-8n - 6} \times \dfrac{9}{9} = \dfrac{-90n + 45}{-72n - 54} $ Multiply the second expression by $\dfrac{-8n - 6}{-8n - 6}$ $ \dfrac{-10}{9} \times \dfrac{-8n - 6}{-8n - 6} = \dfrac{80n + 60}{-72n - 54} $ Therefore $ k = \dfrac{-90n + 45}{-72n - 54} - \dfrac{80n + 60}{-72n - 54} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{-90n + 45 - (80n + 60) }{-72n - 54} $ Distribute the negative sign: $k = \dfrac{-90n + 45 - 80n - 60}{-72n - 54}$ $k = \dfrac{-170n - 15}{-72n - 54}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{170n + 15}{72n + 54}$